


the rational function

by nandayo



Category: Vocaloid
Genre: Alternate Universe - High School, F/M, I just like writing stories with math in them, Len teases, Math, Rin gets flustered, but not too much math don't worry, how does tagging work??, light&sweet, that's how I like to write them usually
Language: English
Status: Completed
Published: 2017-04-25
Updated: 2017-04-25
Packaged: 2018-10-24 00:55:22
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 4,680
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/10730832
Author URL: https://archiveofourown.org/users/nandayo/pseuds/nandayo
Summary: Rin is the snobby math nerd. Len needs math help, badly. The result is irrational as pi. Rin/Len, lots of banter, kinda fluffy.





	the rational function

He just wasn't very smart, she thought.

Once, in seventh grade. They'd all had to prepare a three-minute speech about whatever topic they wanted. Rin had chosen to explain some complex number theory, which she'd read a book about recently. (When she looked back, she cringed at how snobby her topic must have seemed, but she hadn't actually meant to show off or anything. Complex numbers weren't even her favourite, really. It's just what was on her mind at the moment, honest.)

Len had chosen to talk about a book he'd just read, too. Rin didn't remember the title—it was one of those schlocky teeny boy books, for those too edgy for Harry Potter but not patient enough for _real_ sci-fi. All cheap "action" with no thought put into them whatsoever. But it'd been a popular book at the time (probably only because of the movie).

Len's enthusiastic, illustratively gestured speech went two minutes over the time limit even though he was basically just repeating the plot—interjecting with his own meaningless reactions like, "My mind was blown at this part, for real, I could not put it down, it was so amaaaazing, you know?" He didn't condense his summary in any meaningful way and he didn't provide even a single insightful opinion.

Most of the class's speeches were like that, not very well thought out, but for some reason, Rin remembers his as particularly inane.

Then there was a rainy day in grade eight. Assigned seating that month placed him next to her in the corner, shaking legs and drumming pencils and asking her to please read out what the board said on the far right, he didn't bring his glasses today. Though she never _asked_ him to stop with the leg shaking or pencil drumming or glasses forgetting, she disparaged him for it anyway.

He was conspicuously absent that morning. Rin thought idly that he probably couldn't be bothered to go outside in this weather. They were at the age where skipping school was becoming cool, indifference to education becoming admirable.

He slipped in at lunch, when the teacher was gone. Sliding into their corner unnoticed, he side glanced her and asked if she did the math homework, and if she would like a bag of cookies in exchange for her answers.

She looked at him for a long moment. His expression was light, like he didn't _really_ care if he handed in the math homework or if he got another incomplete mark on his record.

She refused his offer with a crisp voice. He looked at her curiously for a moment, then shrugged and opened his cookies.

And then, in ninth grade. It had been a long day for Rin. She'd just gotten back a less-than-stellar mark on a science test, and the friend she usually sat with at lunch forgot her lunch bag at home, obligating Rin to share her sandwich even though she didn't want to, and now she was hungry.

It also happened to be the last day of classes before winter break. As soon as the last bell rang, coats seemed to magically appear on students' backs as they swarmed the doors open. Fluffy snowflakes blew through the crowded halls as biting wind whipped past the threshold, and Rin, not yet in her jacket, bitterly wondered why the administration hadn't installed double doors to stop the draft.

When she arrived at her locker, she was met with a surprise.

Len was standing there, fiddling with her lock.

He turned the dial, yanked the lock, and when it didn't open, he furrowed his brow and tried again. When Rin approached, he was rattling it in frustration.

"What the hell, why isn't it opening?"

"What are you doing?"

"Huh?" His face lit up as he recognized her. The girl who used to sit next to him in grade eight. "My stupid lock has decided to not work today, when I just wanna get out of here as fast as possible."

The halls were emptying fast, their classmates rushing out with visions of Christmas. He returned to shaking her lock, and Rin took a moment to wonder if he was for real.

"You're confused. That's my locker."

She moved closer to nudge him aside, but when she bumped his shoulder with the side of her fist, he glanced up but didn't move, concentrating on re-entering his combination. Rin flushed and bumped harder. Harder than she intended.

"Ow, jeez, what?"

Her face was hot despite the wintry draft. "Look at the number. 1039. That's mine, it's been mine the whole year."

"What are you— Oh. Oh shit." He stepped away from the locker like it was open flame. "How did I— I'm messed up today, sorry."

She didn't look at him as she clicked her lock open. She was grateful the locker door hid her burning face as she reached in for her coat. Then her shoulder bumped something warm—Len was still there, turning the lock of number 1038.

"I switched lockers today and I guess I, uh, remembered the wrong number."

She put her coat on. "How do you mistake 39 for 38? They're two completely different numbers."

"They're right beside each other."

"But they're completely different. It's different from confusing, say, 246 and 264, because they have the same digits and they're both divisible by six—"

He shrugged. A small smile tugged up by perhaps a memory, a meaningless memory of the girl in front of him presenting college math to his seventh-grade class. "Hey, we can't all be smart like you."

It took her a few seconds to decide it made her angry.

* * *

He trailed her outside towards her bus stop. The snow fell thick and heavy, already layered up to their ankles, dotted with footprints from their classmates, long gone home. Where the snow was fresh, Rin tore a path like walking through wet paper.

"So, like, we've known each other for years, but we've never really talked much, huh?"

She didn't answer as the wind stung her cheeks.

He moved up from behind her, tearing his own path parallel to hers.

She glanced down and noticed his sneakers, stained wet and dark. "You're not wearing boots."

"Can't walk in those things."

She'd expected him to grin widely while saying that, but his smile was quieter. A candlelight in the cold, where they walked alone with no one else to see. Four in the afternoon.

* * *

the rational function

_a polynomial over a polynomial; it's like, a fraction_

* * *

So that's why she thought he wasn't very smart.

Now, she didn't care much about how smart someone was (though if you were smart, she was more inclined to care about you)—unless she was paired with them for a school project.

As luck would have it, towards the end of ninth grade, Rin and Len were partnered for a history project. It was one of Rin's worse subjects—the web of people and events and dates never summed up right in her head.

Rin slouched to their meeting place in the library. Len seemed more chipper than the situation called for.

"Let's do this," he said, enthused, as if history wasn't the most boring subject on his schedule. "How about I do research, and you compile it?"

"No, I'll do research, you compile it."

The research was the more important part, of course. It decided the direction of the whole project, and she didn't trust Len to do more "research" than clicking 'Print' on the first three results of his first Google search.

She doubted he even knew the keyboard shortcut to print a webpage.

It was her stern tone, probably, that prompted that curious upward tilt of his chin. She straightened, folded her hands on the table, and rationalized her hasty assertion.

"Well I just thought, the research is the more difficult part, you know? So I'll take it off your shoulders—you'll have more time to yourself then."

She could format her research so that compilation would be very easy for him; he'd barely need to do anything other than cut up her meticulous pages and stick them on a bristol board.

"You don't need to accommodate for me or anything," Len said with a smile, and Rin could hear the kindness in his voice. But she kept firm about it, and then to her uneasy curiosity he began to frown.

"Is it that you don't trust me?"

Her gut squeezed—he was right, of course, but to put it so plainly! Her face began to grow hot, and her hands itched to come up to cover her cheeks, but she stayed resolutely still.

Len continued. "It's just that I've been looking forward to the World War II unit since we got the syllabus. So I would actually be pleased if I got to do the research part." His gaze met hers like shooting an arrow. "I _want_ to do it."

She scrambled to gather her thoughts. "It's not that I don't trust you, that's not it. I just—have you ever done research before? Like _really_ done it, not just printing out Wikipedia."

His mouth hung open a moment. "Wow. Wait, just—how are you such a snob?"

If it was possible for any more blood to flood through her cheeks. For embarrassment, but more anger. When she thought about it, yes, maybe she should've been more tactful, but he could speak for himself!

"Look, look, I'm sorry, I didn't mean it," Len retracted when he saw her expression. "Just forget it, I'm sorry."

"…I didn't mean…" Rin started, "I didn't mean to imply anything about you. I was just, you know, I really care about this project, okay? So I wanted to make sure—"

"Yeah, I get it," he said wryly. "I know people like you. Forget I said anything."

_People like you._

She was shocked to find she was holding back tears. It was just the heat of the moment, she told herself.

Len inhaled through his teeth. "Really, sorry. You can do the research part. Just forget it."

But she wouldn't forget, of course. The surging embarrassment of being judged so openly for the first time. She knew people probably judged her all the time, the same way as Len had, every time she raised her hand in class and every time a teacher gave her a secret smile as they handed back her test. But no one had ever said anything to her face. She'd never heard even a whisper.

* * *

They didn't meet up again for that project. When she'd finished her research, all meticulously formatted and prepared just for him, she'd stuffed it in the crack under locker 1038 and speedwalked away. The both of them ended with an excellent grade, of course.

* * *

It was a great summer without seeing him, but then in the fall, on the first day, she'd decided to work on math in the library after school. (Not the assigned homework, that was too easy, but the challenge problems at the end of each chapter were great fun.)

This was a mistake on her end.

She'd been stuck on problem three for twenty minutes when she heard a thunk from the other side of the table.

She hadn't even noticed him approaching. He'd put his textbooks down on the table and was pulling out the chair across from her. His expression was stolid.

"Hi."

"…Hi."

What was he doing? They weren't exactly friends.

It was that table over there, three tables away, she remembered absently, where they'd been discussing that history project back in June.

His eyes flicked upwards like he was nervous, then he smiled a small, reluctant smile. "Is that math?"

"What does it look like?"

He cringed, but there was curiously some mirth he tried to conceal by rubbing his nose. He peered closer at her open textbook, careful not to lean too far forward. "Um… math. But I dunno, chem and physics have a lot of equations too."

She stared hard at the elusive question three. "I can tell someone hasn't opened his functions book." He didn't even recognize the format of the pages? He was going to fail. But not her problem.

He stifled a scrape of laughter. "Oh my god."

She put her pencil to the page, to begin sketching an answer to three, willfully ignoring him.

"It's true, though," he continued, watching her carefully. "I haven't opened that book."

She scoffed inwardly.

"In fact I haven't even touched it."

She scoffed outwardly.

"In fact I don't even have my own copy of it yet."

This made her look up suddenly. Her eyes were like a vulture's. His lips curled in amusement.

"I have functions next semester," he said lowly.

Rin blinked. Her mouth formed a thin line, holding her words back like a traffic guard. "Right," she muttered. "Right."

It was normal, in a semestered school, for him to not have functions yet. Half the grade didn't have functions yet. She'd gone and jumped to conclusions as usual, and from his smirk, it'd been his intention to mislead her all along.

"So is it fun?" Len said, pretending to brush it off but really, Rin knew, inside he was laughing at her. "Functions? Functions for fun?"

She rolled her eyes hard. " _Idiot_."

"At least I know it," he said lightly, then fingered the edge of her book as he thought of his next words. She glared at his hand but didn't say anything.

"Okay, um, I know it's kind of weird to ask, but…" He sighed. "Are we okay? You know, we could be friends, if you want."

She grit her teeth. "No."

Though uneasy, a slow grin appeared on his face. "You're savage, you know?"

She could not concentrate on question three like this. Stupid, stupid Len. Stupid question three. "Question three is savage."

"Having trouble, are we? Let me see, I can help."

She gave him a withering look.

"I was just joking, obviously."

"You need to work on your jokes, then."

She'd given up on three for now, and moved on to four, which to her relief clicked instantly like clockwork, and the solution detailed in her brain faster than she could write it out. Len watched as her pencil suddenly burst into activity, numbers and symbols popping up on the page like gunfire.

He stayed there watching her for a few more minutes, then he left her in her concentration.

* * *

But he was back the next day.

"Same spot as yesterday," he observed. "Are you making this a routine?"

"I just wait here before my parents can pick me up."

"Don't you usually take the bus, though?"

Her head snapped up then, the same narrow glare as usual—the only times she allowed him her attention were when he said something particularly offensive. "How do you—" Then she remembered that one day with the locker, walking in the snow. He'd walked her up to her bus stop, then continued on, saying his house was just five blocks ahead.

"You remember, right?" he said. "We walked together once—"

"Yeah, yeah," she said irritably. "But I decided it's better to just wait, it saves me the bus fare."

"True."

Silence for a while. She finished two questions. When she looked up again, he was relaxed in his seat, just staring into space like he wasn't a waste of space. "Why are you here," she gritted out, not toning it like a question, but rather an argument.

"Well, you're the only one I know here, and I'm too bored to sit by myself—"

"No, I meant, why are you in the library after school." She brought herself to look at him. "You walk home, don't you?"

He smiled a little, as if surprised she'd thought of that. "I needed to return a book yesterday."

"And today?"

"I was just curious if you'd be here again." He nodded. "Seems you are."

She flipped the page of her notebook rapidly, so cool air hit her face and brushed back her hair. "I'll be here every day."

"Well, yeah, if you're not taking the bus."

Neither of them said anything. The silence sparked. Len stared vacantly at her pencil tip as it did its rapid magic. The dark air of their history project, three tables down, smoked out more and more and then when Len left, it was, for the most part, clear.

* * *

She could not explain the feeling when he didn't appear the next day.

It's just, she'd kind of expected him to come. She didn't know why, it was completely irrational—why would he, anyway? He didn't have a reason to come anymore—return a book? Again? It's not like he read more than one book a month. Check if she was there again? Not now that he knew she was there every day—and he shouldn't have done that in the first place, checking if she was there, that was just creepy! Unnecessary! A flagrant lack of shame!

So why was she so annoyed? She should have been happy that she could do her challenge problems in peace. But she was annoyed, very annoyed, at him and at herself.

So then, for reasons she would rather not contemplate, she decided to not return to the library after school. For the rest of the semester, she went instead to a table in the abandoned cafeteria, where the janitors proved much better company than any boy her age, even if she did have to lift her books up to let them wipe the table.

* * *

Too bad their lockers were beside each other.

Now, Rin never stopped by her locker much; she couldn't be inconvenienced to come all the way down to the first floor between every class when she could just keep all her books in her bag (it really wasn't that heavy, not at all). But when autumn chilled and she started wearing her jacket to school, she was inevitably accosted by the owner of locker 1038.

"Cold, isn't it?"

She shrugged off her jacket, hung it up quickly. Her fingers still felt a bit frozen. "Clearly."

He rolled off his own coat, a deep green sports jacket. "So what class do you have now?"

She was surprised he didn't mention her absence in the library, though it'd been a good while since they'd talked there, so she supposed it made sense. "Math. You?"

"Math first thing in the morning? Why didn't you switch out?" At her frown he rolled his eyes, but not with venom. "I have anthro."

"Anthro."

"It's really birdy," he admitted. "But it's nice to be at ease in class. I can kind of tune out, I can't do that in math or science like you can." When she opened her mouth to say something, he spoke over her. "But of course you don't, because you love the feeling when the teacher says something you already know."

"You're really annoying," she said, pretending to be looking for something in her mostly-empty locker.

"Sorry, sorry," he said lightly.

Rin looked at him closely. He didn't look very sorry. He looked almost as if he were challenging her.

"Not sorry," she parried.

They both shut their lockers.

* * *

The cold was relentless on the way to January. She'd gotten used to seeing Len at the spot between 1038 and 1039, though on some days, when she didn't want to see him, she would purposefully come early enough in the morning and late enough in the afternoon that she wouldn't bump into him.

One afternoon, though, he was there, leaning against her locker, fifteen minutes after the last bell. The halls were deserted.

"You're pretty late," he remarked as she approached. "Were you doing something?"

"Is it your business?" Though she barely said those sorts of things bitingly anymore. Now she said them expressionlessly; still blunt blows, but light.

"I was just asking."

She opened her locker, grabbed her winter things, closed the locker. "Then why are _you_ so late, were _you_ doing something?"

"I wanted to ask you something," he said, and she frowned up at him. He was only the tiniest bit taller than her, and she was sure she would catch up soon, because her growth spurt was yet to come, somewhere in the near future (or so she told herself).

He bounced off the locker, then paused.

"Spit it out, I don't have all day."

"Okay, the thing is… Wait, what did you get in functions last term?"

"Is it your business?" she repeated.

"No, really, what did you get?"

For some reason, she flushed. Normally when people asked her her grades, she would tell them, matter-of-factly but privately proud. She liked seeing their reactions, their gaping mouths, their disbelief. But this was a bit different. She was embarrassed…the memory of a June history project flickering in her mind. "Fifty times two," she muttered, so quietly she thought he couldn't hear, but it seemed he did because his eyes widened, just like everyone else's would have.

"I mean, I wouldn't expect less from you, but to not make a single mistake the whole term? Amazing."

She just stood there, face burning. (But between you and me, her heart skipped when he'd called her amazing—shh.)

"It's not—it's nothing."

He raised a brow at that, and she burned a little more, her feet bending into ashes.

"No, really. You're really amazing."

"It's just that the tests are easy!" she spluttered, voice raising a pitch at the end, and she slapped a hand over her mouth, cursing herself.

Len grinned, wide, holding his laughter in because he didn't want her to explode. "Right, easy for you, but… apparently, not quite as easy for me." He looked at her meaningfully. "So, um. Would you mind, you know?"

"What?" she said weakly, her tone a small whine. Like a little piglet. He suddenly felt like reaching out and patting her head.

"Helping me out? You're free after school anyway, right?"

In retrospect, she decided she'd only agreed because she was so damn out of it by then.

* * *

At the same library table as before, she pored over his recent tests. Fifty, forty, thirty-two.

"You need help," she agreed. He groaned.

"Well, what is it you don't get?" she asked. "To be honest I don't know where to start. Do we have to go back to the beginning?"

He winced. "If necessary."

She shook her head, but she was smiling. "Okay, um… I've never really taught anyone before, but… Let's just go over these tests first?"

Rin had been uncertain at first, but she found that Len was surprisingly easy to teach. Yes, when they first settled at the table every day, he'd begin the usual jibes, but when she coughed and looked at him seriously, he transformed into a good listener. After a week or so, Len could do most of the assigned problems with little difficulty. (With a little nudging in the right direction from her end.) He deserved a gold star or two.

She'd been expecting more trouble, more frustration. There was some annoyance when she had to explain the simplest things more than once ("If the denominator is zero it's undefined, Len, you draw an asymptote here, how do you not remember this, this is the fifth time!"), but on the whole, it was easier than she expected. Len really wasn't that bad. She told him so. He waggled his brows. She mouthed, "Thirty-two," which sobered him up.

"Why are you doing so badly though?" She had to wonder as she checked his solutions. All correct. "Who's your teacher?"

"Besides you, you mean? Sakine. She's… you know."

"I see. I mean, I had her too, but the textbook is good enough to learn from. At least, it was enough for me."

"You'd be fine even without the textbook."

"And go without my challenge problems? I'd die of boredom."

"You're not being sarcastic."

"What, it's fun!"

"You're crazy," he scoffed. "I really, really don't understand people who think this is fun."

"It's because you haven't mastered the basics," she explained earnestly. "Once you can do the basic stuff really well, it'll all start making sense in your head. It comes together, and it's all like a set of tools. And then, when you look at a challenge problem—they're ones like you've never seen before. You can't just plug in numbers or whatever, you really have to think about them. And it's wonderful because you have your tools, and you have to stretch your mind to find out how to use them in ways you've never seen before to solve this new problem."

"Careful, your eyes are sparkling."

"It's like art," she said emphatically. "You just have to learn the theory first, the techniques, the history… How to choose colours and how to pick a brush."

He was silent for a long moment. Then he said, "You know, I was wrong about you."

Caught midair in her enthusiasm, she fell to the ground suddenly. "Wrong about what?"

"Well, no, I wasn't wrong, exactly," he amended. "I thought you were a complete snob. And you are." He pressed on before she could protest. "But I guess… you're like math to me."

She was aghast, to say the least. "And you're like a bucket of dead fish to me. Your point?"

He shook his head, smiling. "What I mean is, I never really liked math, but when you explain it like that, your enthusiasm really shines through. And I realized, even if math isn't really my thing, like you said, it has its good points."

A long conversation passed by way of their eyes. Irritation. Honest, earnest. _Idiot_. A shrug. A small smile, laughter.

She muttered something.

"What? I didn't catch that."

Her mouth moved, but no sound came out.

"Speak up."

It was painful to meet his gaze, but she forced her grimace away and faced him head on. "I always judged you too, I guess. But really, you're smart in your own way."

"…What's that supposed to mean?"

"What do you think it means?!"

"You think I'm smart?"

"No, I didn't say that. You're not _smart_. You don't even remember exponent laws, for one thing. And if you were smart you would've never talked to me after that history thing—"

"You think? But I think it's one of the smartest things I've done."

Her heart was erratic. "Really."

Crinkles at the sides of his eyes. "Yeah, 'cause I won't fail functions now."

* * *

the rational function

_a fraction of you_

* * *

(omake)

He'd gotten a seventy-five on his next test. Rin was smug.

"I wonder how you'll thank me," she said. "I didn't even charge you for, how many hours did I spend on you? I should've charged, I should've."

"Right," he said without enthusiasm. "Well, what do you want?"

She hadn't expected that; she didn't expect him to offer anything. She quietened. "Um, money?"

"And what would you spend it on?"

She thought seriously about it. "Well, there's nothing I've really wanted recently. I'd buy you boots, maybe."

He smiled despite himself. "You'd spend it on me?"

"No. It's just your feet stink 'cause your socks are wet. Seriously, go buy boots. Or at least waterproof shoes."

"If you insist." Then an idea came to him, and he added, "Come with me to buy them?"

Caught her off guard again. "You can't go yourself?"

"I could, but really, come."

"You could, really, go yourself."

"No seriously, I'm asking you to come."

He enjoyed watching her get more and more flustered. He felt it was a divine ability, to get her this visibly squeamish.

"No, seriously, I'm saying no. Go yourself."

"Saturday. No, Friday, after school?"

"Nooooo," she said, but she trailed off as her voice fizzled away and she turned weakly to the opposite wall. He knew he'd won then.

"We can catch a movie too," he added as an afterthought (but really it'd been his first thought).

Rin put her head on the desk, muffling her voice. " _…really are stupid._ "

**Author's Note:**

> Hi, sooo you might know me from ffnet, you probably don't, but I am crossposting this from there, this is my Ao3 account, how does this site work I am a lost child :< does anyone even go on this site???  
> thanks for reading :)


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